I thought I had logged into the Appstore already and was having difficulty finding the re-download option and was scared by all the buttons saying it would cost me $30 USD to download it.

Problem solved. In summary, yes, you have to upgrade to OSX 10.6.8 (made easy for me as I still had the disk from my previous upgrade) then login to the Mac App Store, then re-install OSX 10.7.1, then update, and then, and only then, was I able to restore my old files from my Time Machine backup.